Exam 3: Generalization: How Broadly Do the Results Apply

In June of 2012, New York City Mayor Michael Bloomberg proposed banning the sale of any reg-ular soda or other sugary drinks in containers larger than 16 oz. A fast food chain polled a random sample of 2500 of its regular customers and found that 63% opposed the ban, 28% supported the ban, and 9% had no opinion. -Is this sample representative of the population of ALL New York City residents?

In June of 2012, New York City Mayor Michael Bloomberg proposed banning the sale of any reg-ular soda or other sugary drinks in containers larger than 16 oz. A fast food chain polled a random sample of 2500 of its regular customers and found that 63% opposed the ban, 28% supported the ban, and 9% had no opinion. -What type of plot would be most appropriate to display these data?

A hot dog manufacturer asserts that one of its brands of hot dogs has an average fat content of 18grams per hot dog. Fat contents in hot dogs from this manufacturer follow an approximately normal distribution with a standard deviation of 1.1grams. Define the statisticx ̅ = mean fat content in a random sample of 10 hot dogs. -Is the sampling distribution of approximately normal?

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food is seals and other marine animals, which they hunt from a platform of sea ice. Scientists are concerned that global warming is melting these platforms earlier in the year, reducing the time polar bears are able to hunt and forcing them inland without the necessary fat reserves built up to survive summer and fall. The US Geological Survey (USGS) conducted a study in the Southern Beaufort Sea to investigate whether climate change has appeared to negatively impact the weight of polar bears. Eighty-three adult male polar bears were captured between March and May of the years 1990 and 2006 and their weights were recorded. The sample mean weight was 324.6 kg, and the sample standard deviation was 88.3 kg. -A histogram of the 83 polar bear weights in the sample is shown below. Are the validity conditions for theory-based inference met for these data?

In June of 2012, New York City Mayor Michael Bloomberg proposed banning the sale of any reg-ular soda or other sugary drinks in containers larger than 16 oz. A fast food chain polled a random sample of 2500 of its regular customers and found that 63% opposed the ban, 28% supported the ban, and 9% had no opinion. -The 2500 regular fast food chain customers surveyed are the ___.

For a survey on affirmative action, researchers selected a random sample of 20 faculty members from a large research university. Faculty in the sample were asked, "Do you favor or oppose using race, religion, sex, color, ethnicity, or national origin as a criterion for college admission?" -Which statistic is appropriate for summarizing these data?

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food are seals and other marine animals, which they hunt from a platform of sea ice. Scientists are concerned that global warming is melting these platforms earlier in the year, reducing the time polar bears are able to hunt and forcing them inland without the necessary fat reserves built up to survive summer and fall. The US Geological Survey (USGS) conducted a study in the Southern Beaufort Sea to investigate whether climate change has appeared to negatively impact the weight of polar bears. Eighty-three adult male polar bears were captured between March and May of the years 1990 and 2006 and their weights were recorded. The sample mean weight was 324.6 kg, the sam-ple median weight was 339.4 kg, and the sample standard deviation was 88.3 kg. A box plot of the data is shown below. -The mean weight in the data set is 324.6 kg, the median weight is 339.4 kg, and the sample standard deviation is 88.3 kg. Which of the following statements do we know to be true based on these values alone? The average weight of all adult male polar bears in the Southern Beaufort Sea is 324.6 kg. ______ (1) The distribution of weights in the sample is roughly symmetric, since the mean and median are close relative to the size of the standard deviation.______ (2) There is evidence that the average weight of an adult male polar bear in the Southern Beaufort Sea is less than 370 kg.______ (3) On average, each adult male polar bear captured weighed 88.3 kg more or less than 324.6 kg.______ (4) Drop-down options for (1), (2), (3), (4): •True •False

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food is seals and other marine animals, which they hunt from a platform of sea ice. Scientists are concerned that global warming is melting these platforms earlier in the year, reducing the time polar bears are able to hunt and forcing them inland without the necessary fat reserves built up to survive summer and fall. The US Geological Survey (USGS) conducted a study in the Southern Beaufort Sea to investigate whether climate change has appeared to negatively impact the weight of polar bears. Eighty-three adult male polar bears were captured between March and May of the years 1990 and 2006 and their weights were recorded. The sample mean weight was 324.6 kg, and the sample standard deviation was 88.3 kg. -What are the appropriate null and alternative hypotheses to investigate whether climate change has appeared to negatively impact the weight of polar bears?

Adult male polar bears are expected to weigh, on average, 370 kg. A polar bear's primary source of food is seals and other marine animals, which they hunt from a platform of sea ice. Scientists are concerned that global warming is melting these platforms earlier in the year, reducing the time polar bears are able to hunt and forcing them inland without the necessary fat reserves built up to survive summer and fall. The US Geological Survey (USGS) conducted a study in the Southern Beaufort Sea to investigate whether climate change has appeared to negatively impact the weight of polar bears. Eighty-three adult male polar bears were captured between March and May of the years 1990 and 2006 and their weights were recorded. The sample mean weight was 324.6 kg, and the sample standard deviation was 88.3 kg. -Do these results provide evidence that the true mean weight of polar bears is less than 370 kg?

A hot dog manufacturer asserts that one of its brands of hot dogs has an average fat content of 18grams per hot dog. Fat contents in hot dogs from this manufacturer follow an approximately normal distribution with a standard deviation of 1.1grams. Define the statisticx ̅ = mean fat content in a random sample of 10 hot dogs. -If we were to select a random sample of 50 hot dogs rather than 10, which of the following features of the sampling distribution of would change? The mean would ______. (1) The shape would ______. (2) The standard deviation would ______. (3) Drop-down options for (1), (2), and (3): •increase •decrease •remain the same

In June of 2012, New York City Mayor Michael Bloomberg proposed banning the sale of any reg-ular soda or other sugary drinks in containers larger than 16 oz. A fast food chain polled a random sample of 2500 of its regular customers and found that 63% opposed the ban, 28% supported the ban, and 9% had no opinion. -The value 63% is a___.

Noxious weeds are invasive plants that quickly spread and deplete the soil of nutrients that are required for all aspects of farming and ranching. With much at stake, the state of Montana has hired a team of researchers to explore the issue. They want to know the average number of noxious weeds per acre in North Central Montana. To do so, researchers divided the area of interest into 1,000,000 acres and randomly selected 24 of these acres. For each selected acre, they counted and removed the noxious weeds. The sample mean was 103.47 weeds, and the sample standard deviation was 46.034 weeds. Below is the simulated bootstrap distribution of 1,000 sample means they created from resampling the observed data. -How was one bootstrapped sample generated in the plot above?

A rental car company has noticed that the distribution of the number of miles customers put on rental cars per day is skewed to the right, with some occasional high outliers. The distribution has a mean of 80 miles and a standard deviation of 50 miles. -Which of the following distributions would have the smallest standard deviation?

A histogram of a bootstrapped null distribution is shown below. Based on these results, what is the strength of evidence against the null hypothesis?

The following histogram shows the distribution of the difference between the actual and "ideal" weights for 119 female students. Ideal weights are responses to the question "What is your ideal weight"? The difference = actual - ideal. -How does the mean compare to the median in this data set?

A rental car company has noticed that the distribution of the number of miles customers put on rental cars per day is skewed to the right, with some occasional high outliers. The distribution has a mean of 80 miles and a standard deviation of 50 miles. -Which of the following distributions most likely match the shape of the distribution of the number of miles customers put on rental cars per day for this rental car company?

If the sample size is larger than 20 and the sample distribution is not strongly skewed, then the sampling distribution of the sample median will be approximately normal.

Most experts recommend college students get at least 8 hours of sleep per night. You collect a random sample of 112 students at your college and ask how many hours of sleep they got last night. The sample mean amount of sleep last night was 7.6 hours, with a sample standard deviation of 2.1 hours. The sample distribution of hours of sleep was slightly skewed right. Does this provide evidence that students at your college are getting less than the recommended amount of sleep per night? -Is the value 7.6 hours a parameter or a statistic? What is its appropriate symbol?

Noxious weeds are invasive plants that quickly spread and deplete the soil of nutrients that are required for all aspects of farming and ranching. With much at stake, the state of Montana has hired a team of researchers to explore the issue. They want to know the average number of noxious weeds per acre in North Central Montana. To do so, researchers divided the area of interest into 1,000,000 acres and randomly selected 24 of these acres. For each selected acre, they counted and removed the noxious weeds. The sample mean was 103.47 weeds, and the sample standard deviation was 46.034 weeds. Below is the simulated bootstrap distribution of 1,000 sample means they created from resampling the observed data. -How could you use the bootstrapped distribution to calculate a p-value to test whether the mean number of noxious weeds in North Central Montana is larger than 90 weeds per acre?

Suppose that the proportion of all American adults that fit the medical definition of being obese is 0.23. A large medical clinic would like to determine if the proportion of their patients that are obese is higher than that of all American adults. The clinic takes a simple random sample of 30 of their patients and finds that 9 patients in the sample are obese. -The researchers created the following simulated null distribution with 1000 trials using the One Proportion applet: What is the appropriate label for the x-axis of the randomization distribution plot?